 This Slideshow was developed to accompany the textbook  Larson Algebra 2  By Larson, R., Boswell, L., Kanold, T. D., & Stiff, L.  2011 Holt McDougal  Some examples and diagrams are taken from the textbook. Slides created by Richard Wright, Andrews Academy Slides created by Richard Wright, Andrews Academy

 Sequence  Function whose domain are integers  List of numbers that follow a rule  2, 4, 6, 8, 10  Finite  2, 4, 6, 8, 10, …  Infinite

 To graph  n is like x; a n is like y  The graph will be dots  Do NOT connect the dots

 Series  Sum of a sequence  2, 4, 6, 8, …  sequence  · · ·  series

Index of summation (variable) Lower limit Upper limit

 12.1 Homework Quiz 12.1 Homework Quiz

 Arithmetic Sequences  Common difference (d) between successive terms  Add the same number each time  3, 6, 9, 12, 15, …  d = 3  Is it arithmetic?  -10, -6, -2, 0, 2, 6, 10, …  5, 11, 17, 23, 29, …

 Write a rule for the n th term  32, 47, 62, 77, …  Formula for n th term  a n = a 1 + (n – 1)d

 One term of an arithmetic sequence is a 8 = 50. The common difference is Write the rule for the n th term.

 Two terms of an arithmetic sequence are a 5 = 10 and a 30 = 110. Write a rule for the n th term.

 Consider the arithmetic series  ···  Find the sum of the first 25 terms.

 Consider the arithmetic series  ···  Find n such that S n = -760  806 #3-63 every other odd, = 20

 12.2 Homework Quiz 12.2 Homework Quiz

 Created by multiplying by a common ratio (r)  Are these geometric sequences?  1, 2, 6, 24, 120, …  81, 27, 9, 3, 1, …

 Write a rule for the n th term and find a 8.  5, 2, 0.8, 0.32, …  Formula for n th term  a n = a 1 ·r n-1

 One term of a geometric sequence is a 4 = 3 and r = 3. Write the rule for the n th term.

 If two terms of a geometric sequence are a 2 = -4 and a 6 = -1024, write rule for the n th term.

 Find the sum of the first 10 terms of  ½ + ···

 Find n such that S n = 31/4  ½ + ···  814 #3-47 every other odd, 49, 51, 53, 57, = 20

 12.3 Homework Quiz 12.3 Homework Quiz

What is the sum of the pieces if we keep cutting forever?

 An infinite geometric series has a 1 = 5 has sum of 27/5. Find the common ratio.

 Write … as a fraction.

 Write … as a fraction.  823 #3-33 odd, 37, 39, = 20

 12.4 Homework Quiz 12.4 Homework Quiz

 Explicit Rule  Gives the n th term directly  a n = 2 + 4n  Recursive Rule  Each term is found by knowing the previous term  a 1 = 6; a n = a n-1 + 4

 a 1 = 2, a 2 = 2, a n = a n-2 – a n-1  Write the first 5 terms  a 1 = 1, a n = (a n-1 ) 2 + 1

 Write the rules for the arithmetic sequence where a 1 = 15 and d = 5.  Explicit  Recursive

 Write the rule for the geometric sequence where a 1 = 4 and r = 0.2  Explicit  Recursive

 1, 2, 2, 4, 8, 32, …  Write a recursive rule for  1, 1, 4, 10, 28, 76, …

 Iterations  Repeated composition of functions  f(f(f(x)))  Use x to find f(x)  Use that value to find the next f(x)  x 1 = f(x 0 ); x 2 = f(x 1 ), …  Find the first three iterations of the function.  f(x) = 4x – 3, x 0 = 2  830 #3-31 odd, odd, 43, = 25

 12.5 Homework Quiz 12.5 Homework Quiz

 843 #choose 20 = 20